Swarms of low-cost autonomous robots can potentially be used to collectively perform tasks over v... more Swarms of low-cost autonomous robots can potentially be used to collectively perform tasks over very large domains and time scales. Novel robots for swarm applications are currently being developed as a result of recent advances in sensing, actuation, processing, power, and manufacturing. These platforms can be used by researchers to conduct experiments with robot collectives and by educators to include robotic hardware in their curricula. However, existing low-cost robots are specialized and can lack desired sensing, navigation, control, and manipulation capabilities. This paper presents a new mobile robot platform, Pheeno, that is affordable, versatile, and suitable for multi-robot research, education, and outreach activities. Users can modify Pheeno for their applications by designing custom modules that attach to its core module. We describe the design of the Pheeno core and a three degree-of-freedom gripper module, which enables unprecedented manipulation capabilities for a robot of Pheeno's size and cost. We experimentally demonstrate Pheeno's ability to fuse measurements from its onboard odometry for global position estimation and use its camera for object identification in real time. We also show that groups of two and three Pheenos can act on commands from a central controller and consistently transport a payload in a desired direction.
Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective t... more Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective transport strategies that are decentralized, scalable, and do not require a priori information about the payload. We investigate this phenomenon in Aphaenogaster cockerelli in order to extract the ants' roles during transport, the rules that govern their actions, and the individual forces that they apply to guide a food item to their nest. To measure these forces, we designed and fabricated elastic structures with calibrated stiffness properties, induced ants to retrieve the structures, and tracked the resulting deformations with a camera. We then developed a hybrid system model of the ant behaviors that were observed in the experiments. We conducted simulations of the behavioral model that incorporate a quasistatic model of planar manipulation with compliant attachment points. Our simulations qualitatively replicate individual ant activity as well as certain macroscopic features of the transport.
In this paper, we consider the problem of optimally guiding a large-scale swarm of underwater veh... more In this paper, we consider the problem of optimally guiding a large-scale swarm of underwater vehicles that is tasked with the indirect control of an advection-diffusion environmental field. The microscopic vehicle dynamics are governed by a stochastic differential equation with drift. The drift terms model the self-propelled velocity of the vehicle and the velocity field of the currents. In the mean-field setting, the macroscopic vehicle dynamics are governed by a Kolmogorov forward equation in the form of a linear parabolic advection-diffusion equation. The environmental field is governed by an advection-diffusion equation in which the advection term is defined by the fluid velocity field. The vehicles are equipped with on-board actuators that enable the swarm to act as a distributed source in the environmental field, modulated by a scalar control parameter that determines the local source intensity. In this setting, we formulate an optimal control problem to compute the vehicle velocity and actuator intensity fields that drive the environmental field to a desired distribution within a specified amount of time. In other words, we design optimal vector and scalar actuation fields to indirectly control the environmental field through a distributed source, produced by the swarm. After proving an existence result for the solution of the optimal control problem, we discretize and solve the problem using the Finite Element Method (FEM). The FEM discretization naturally provides an operator that represents the bilinear way in which the controls enter into the dynamics of the vehicle swarm and the environmental field. Finally, we show through numerical simulations the effectiveness of our control strategy in regulating the environmental field to zero or to a desired distribution in the presence of a double-gyre flow field.
In this paper, we propose a computationally efficient, robust density control strategy for the me... more In this paper, we propose a computationally efficient, robust density control strategy for the mean-field model of a robotic swarm. We formulate a static optimal control problem (OCP) that computes a robot velocity field which drives the swarm to a target equilibrium density, and we prove the stability of the controlled system in the presence of transient perturbations and uncertainties in the initial conditions. The density dynamics are described by a linear elliptic advection-diffusion equation in which the control enters bilinearly into the advection term. The well-posedness of the state problem is ensured by an integral constraint. We prove the existence of optimal controls by embedding the state constraint into the weak formulation of the state dynamics. The resulting control field is space-dependent and does not require any communication between robots or costly density estimation algorithms. Based on the properties of the primal and dual systems, we first propose a method to accommodate the state constraint. Exploiting the properties of the state dynamics and associated controls, we then construct a modified dynamic OCP to speed up the convergence to the target equilibrium density of the associated static problem. We then show that the finite-element discretization of the static and dynamic OCPs inherits the structure and several useful properties of their infinite-dimensional formulations. Finally, we demonstrate the effectiveness of our control approach through numerical simulations of scenarios with obstacles and an external velocity field.
In this paper, we propose a fully decentralized control strategy for collective payload transport... more In this paper, we propose a fully decentralized control strategy for collective payload transport in 3D space by a team of identical holonomic mobile robots in a microgravity environment. This task has potential space applications such as on-orbit assembly, debris removal, and planetary construction, which have to be performed in uncertain environments where inter-robot communication is unreliable or not available. Decentralized control schemes that rely on limited data and do not require inter-robot communication would enable teams of robots to achieve cooperative transport objectives in unknown environments. Existing decentralized strategies for collective payload transport require at least some of the following information: (1) the geometry and dynamics of the payload; (2) the payload's position and velocity over time; (3) the number and distribution of robots around the payload; (4) the vector from the payload's center of mass to each robot's attachment point; and (5) desired trajectories for the robots and payload. In this paper, we consider a team of robots that must stabilize a payload's center of mass to a target position without access to any of this information. The robots are assumed to be rigidly attached to the payload, e.g. via pincers, grippers, or magnets, and the only information provided to them is the target position in a global coordinate system that is shared by all the robots. The robots do not exchange information and only require measurements of their own positions and velocities. Moreover, the payload may have an arbitrary shape, without particular constraints on its geometry (e.g., convexity). Given these assumptions and objectives, and building on our prior work on collective transport strategies, we design a fully decentralized proportional-derivative controller that can be employed by the robots to drive the payload's center of mass to the destination. Using a Lyapunov stability argument, we analytically prove that under this controller, the payload's center of mass asymptotically converges to a small neighborhood of the target position. The radius of this neighborhood is the magnitude of the error between the target position and actual steady-state position of the payload's center of mass. We also investigate the effect of the distribution of robots around the payload on the magnitude of this error. We validate our theoretical results in MATLAB simulations of five collective transport scenarios with different payload shapes and variations in the distribution of robots around the payload.
In this paper, we propose decentralized position controllers for a team of point-mass robots that... more In this paper, we propose decentralized position controllers for a team of point-mass robots that must cooperatively transport a payload to a target location. The robots have double-integrator dynamics and are rigidly attached to the payload. The controllers only require robots' measurements of their own positions and velocities, and the only information provided to the robots is the desired position of the payload's center of mass. We consider scenarios in which the robots do not know the position of the payload's center of mass and try to selfishly stabilize their own positions to the desired location, similar to the behaviors exhibited by certain species of ants when retrieving food items in groups. We propose a proportional-derivative (PD) controller that does not rely on inter-robot communication, prior information about the load dynamics and geometry, or knowledge of the number of robots and their distribution around the payload. Using a Lyapunov argument, we prove...
In this paper, we propose an obstacle avoidance controller for a disk-shaped holonomic robot with... more In this paper, we propose an obstacle avoidance controller for a disk-shaped holonomic robot with double-integrator dynamics and local sensing. The control objective is for the robot to converge to a target velocity while avoiding collisions with strictly convex obstacles in an unbounded environment. We assume that the robot has no information about the location and geometry of the obstacles, has no localization capabilities, and can only measure its own velocity and its relative position vector to the closest point on any obstacles in its sensing range. We first propose a potential-based controller for the case with a single obstacle, and we prove that the robot safely navigates past the obstacle and attains the desired velocity. For the case with multiple obstacles, we propose a switching control scheme in which the robot applies the single-obstacle controller for the closest obstacle at each instant. We investigate the correctness of this switching control law and demonstrate the absence of local stable equilibrium points that would trap the robot. We validate our analytical results through simulations of a robot that uses the proposed controllers to successfully navigate through an environment with strictly convex obstacles of various shapes and sizes.
This paper presents a novel procedure for computing parameters of a robotic swarm that guarantee ... more This paper presents a novel procedure for computing parameters of a robotic swarm that guarantee coverage performance by the swarm within a specified error from a target spatial distribution. The main contribution of this paper is the analysis of the dependence of this error on two key parameters: the number of robots in the swarm and the robot sensing radius. The robots cannot localize or communicate with one another, and they exhibit stochasticity in their motion and task-switching policies. We model the population dynamics of the swarm as an advection-diffusion-reaction partial differential equation (PDE) with time-dependent advection and reaction terms. We derive rigorous bounds on the discrepancies between the target distribution and the coverage achieved by individualbased and PDE models of the swarm. We use these bounds to select the swarm size that will achieve coverage performance within a given error and the corresponding robot sensing radius that will minimize this error. We also apply the optimal control approach from our prior work in [13] to compute the robots' velocity field and task-switching rates. We validate our procedure through simulations of a scenario in which a robotic swarm must achieve a specified density of pollination activity over a crop field.
In this work, we analyze stochastic coverage schemes (SCS) for robotic swarms in which the robots... more In this work, we analyze stochastic coverage schemes (SCS) for robotic swarms in which the robots randomly attach to a onedimensional boundary of interest using local communication and sensing, without relying on global position information or a map of the environment. Robotic swarms may be required to perform boundary coverage in a variety of applications, including environmental monitoring, collective transport, disaster response, and nanomedicine. We present a novel analytical approach to computing and designing the statistical properties of the communication and sensing networks that are formed by random robot configurations on a boundary. We are particularly interested in the event that a robot configuration forms a connected communication network or maintains continuous sensor coverage of the boundary. Using tools from order statistics, random geometric graphs, and computational geometry, we derive formulas for properties of the random graphs generated by robots that are independently and identically distributed along a boundary. We also develop order-of-magnitude estimates of these properties based on Poisson approximations and threshold functions. For cases where the SCS generates a uniform distribution of robots along the boundary, we apply our analytical results to develop a procedure for computing the robot population size, diameter, sensing range, or communication range that yields a random communication network or sensor network with desired properties.
Experimental Study and Modeling of Group Retrieval in Ants as an Approach to Collective Transport in Swarm Robotic Systems This study finds that ants can act independently to accomplish complex tasks; application of models derived from ant behavior to robotic systems is investigated
2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2011
We present a scalable approach to optimizing robot control policies for a target collective behav... more We present a scalable approach to optimizing robot control policies for a target collective behavior in a spatially inhomogeneous robotic swarm. The approach can incorporate robot feedback to maintain system performance in an unknown environmental flow field. We consider systems in which the robots follow both deterministic and random motion and transition stochastically between tasks. Our methodology is based on an abstraction of the swarm to a macroscopic continuous model, whose dimensionality is independent of the population size, that describes the expected time evolution of swarm subpopulations over a discretization of the environment. We incorporate this model into a stochastic optimization method and map the optimized model parameters onto the robot motion and task transition control policies to achieve a desired global objective. We illustrate our methodology with a scenario in which the behaviors of a swarm of robotic bees are optimized for both uniform and nonuniform pollination of a blueberry field, including in the presence of an unknown wind.
We do a Probabilistic Analysis of the Network generated by robots involved in Stochastic Boundary... more We do a Probabilistic Analysis of the Network generated by robots involved in Stochastic Boundary Coverage
Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective t... more Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective transport strategies that are decentralized, scalable, and do not require a priori information about the payload. We investigate this phenomenon in Aphaenogaster cockerelli in order to extract the ants' roles during transport, the rules that govern their actions, and the individual forces that they apply to guide a food item to their nest. To measure these forces, we designed and fabricated elastic structures with calibrated stiffness properties, induced ants to retrieve the structures, and tracked the resulting deformations with a camera. We then developed a hybrid system model of the ant behaviors that were observed in the experiments. We conducted simulations of the behavioral model that incorporate a quasistatic model of planar manipulation with compliant attachment points. Our simulations qualitatively replicate individual ant activity as well as certain macroscopic features of the transport.
We present a new algorithm for the reachability analysis of multi-affine hybrid systems. In our p... more We present a new algorithm for the reachability analysis of multi-affine hybrid systems. In our previous work on reachability analysis and that of our collaborators [1-3], we exploited the convexity of multiaffine functions and the fact that the vector field in modes with rectangular invariants is uniquely determined by its values at the rectangle vertices. In this paper, we explicitly calculate conical overapproximations of the reachable set in the invariant of each mode. We describe our Multi-Affine Reachability analysis using Conical Overapproximations, Marco, and show that it yields results that are superior to those obtained by existing methods for multi-affine hybrid systems. Finally, we demonstrate the application of Marco to the analysis of an ant house hunting model that incorporates quorum sensing [4] and the analysis of bi-stability of the lactose induction system regulated by glucose and lactose [5].
Proceedings of the 16th international conference on Hybrid systems: computation and control, 2013
Collective food transport in ant colonies is a striking, albeit poorly understood, example of coo... more Collective food transport in ant colonies is a striking, albeit poorly understood, example of coordinated group behavior in nature that can serve as a template for robust, decentralized multi-robot cooperative manipulation strategies. We
We present a methodology for characterizing, analyzing, and synthesizing swarm behaviors using bo... more We present a methodology for characterizing, analyzing, and synthesizing swarm behaviors using both a macroscopic continuous model that represents a swarm as a continuum and a macroscopic discrete model that enumerates individual agents. Our methodology is applied to a dynamical model of ant house hunting, a decentralized process in which a colony attempts to emigrate to the best site among several alternatives. The model is hybrid because the colony switches between different sets of behaviors, or modes, during this process. Using the model in [1], we investigate the relation of site population growth to initial system state with an algorithm called Multi-Affine Reachability analysis using Conical Overapproximations (Marco) [2]. We then derive a microscopic hybrid dynamical model of an agent that respects the specifications of the global behavior at the continuous level. Our multi-level simulations demonstrate that we have produced a rigorously correct microscopic model from the macroscopic descriptions.
Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
We present a methodology for characterizing and synthesizing swarm behaviors using both a macrosc... more We present a methodology for characterizing and synthesizing swarm behaviors using both a macroscopic model that represents a swarm as a continuum and a microscopic model that represents individual robots. We develop a systematic approach for synthesizing behaviors at the macroscopic level that can be realized on individual robots at the microscopic level. Our methodology is inspired by a dynamical model of ant house hunting [1], a decentralized process in which a colony attempts to emigrate to the best site among several alternatives. The model is hybrid because the colony switches between different sets of behaviors, or modes, during this process. At the macroscopic level, we are able to synthesize controllers that result in the deployment of a robotic swarm in a predefined ratio between distinct sites. We then derive hybrid controllers for individual robots using only local interactions and no communication that respect the specifications of the global continuous behavior. Our simulations demonstrate that our synthesis procedure yields a correct microscopic model from the macroscopic description with guarantees on performance at both levels.
2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2007
We present an approach for the dynamic assignment and reassignment of a large team of homogeneous... more We present an approach for the dynamic assignment and reassignment of a large team of homogeneous robotic agents to multiple locations with applications to search and rescue, reconnaissance and exploration missions. Our work is inspired by experimental studies of ant house hunting and empirical models that predict the behavior of the colony that is faced with a choice between multiple candidate nests. We design stochastic control policies that enable the team of agents to distribute themselves between multiple candidate sites in a specified ratio. Additionally, we present an extension to our model to enable fast convergence via switching behaviors based on quorum sensing. The stability and convergence properties of these control policies are analyzed and simulation results are presented.
2008 47th IEEE Conference on Decision and Control, 2008
We present a decentralized, communication-less approach to the dynamic allocation of a swarm of h... more We present a decentralized, communication-less approach to the dynamic allocation of a swarm of homogeneous robots to a target distribution among multiple sites. Building on our work in [1], we optimize stochastic control policies for the robots that cause the population to quickly redistribute among the sites while adhering to a limit on inter-site traffic at equilibrium. We propose a way to account for delays due to navigation between sites in our controller synthesis procedure. Control policies that are designed with and without the use of delay statistics are compared for a simulation in which 240 robots distribute themselves among four buildings.
Swarms of low-cost autonomous robots can potentially be used to collectively perform tasks over v... more Swarms of low-cost autonomous robots can potentially be used to collectively perform tasks over very large domains and time scales. Novel robots for swarm applications are currently being developed as a result of recent advances in sensing, actuation, processing, power, and manufacturing. These platforms can be used by researchers to conduct experiments with robot collectives and by educators to include robotic hardware in their curricula. However, existing low-cost robots are specialized and can lack desired sensing, navigation, control, and manipulation capabilities. This paper presents a new mobile robot platform, Pheeno, that is affordable, versatile, and suitable for multi-robot research, education, and outreach activities. Users can modify Pheeno for their applications by designing custom modules that attach to its core module. We describe the design of the Pheeno core and a three degree-of-freedom gripper module, which enables unprecedented manipulation capabilities for a robot of Pheeno's size and cost. We experimentally demonstrate Pheeno's ability to fuse measurements from its onboard odometry for global position estimation and use its camera for object identification in real time. We also show that groups of two and three Pheenos can act on commands from a central controller and consistently transport a payload in a desired direction.
Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective t... more Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective transport strategies that are decentralized, scalable, and do not require a priori information about the payload. We investigate this phenomenon in Aphaenogaster cockerelli in order to extract the ants' roles during transport, the rules that govern their actions, and the individual forces that they apply to guide a food item to their nest. To measure these forces, we designed and fabricated elastic structures with calibrated stiffness properties, induced ants to retrieve the structures, and tracked the resulting deformations with a camera. We then developed a hybrid system model of the ant behaviors that were observed in the experiments. We conducted simulations of the behavioral model that incorporate a quasistatic model of planar manipulation with compliant attachment points. Our simulations qualitatively replicate individual ant activity as well as certain macroscopic features of the transport.
In this paper, we consider the problem of optimally guiding a large-scale swarm of underwater veh... more In this paper, we consider the problem of optimally guiding a large-scale swarm of underwater vehicles that is tasked with the indirect control of an advection-diffusion environmental field. The microscopic vehicle dynamics are governed by a stochastic differential equation with drift. The drift terms model the self-propelled velocity of the vehicle and the velocity field of the currents. In the mean-field setting, the macroscopic vehicle dynamics are governed by a Kolmogorov forward equation in the form of a linear parabolic advection-diffusion equation. The environmental field is governed by an advection-diffusion equation in which the advection term is defined by the fluid velocity field. The vehicles are equipped with on-board actuators that enable the swarm to act as a distributed source in the environmental field, modulated by a scalar control parameter that determines the local source intensity. In this setting, we formulate an optimal control problem to compute the vehicle velocity and actuator intensity fields that drive the environmental field to a desired distribution within a specified amount of time. In other words, we design optimal vector and scalar actuation fields to indirectly control the environmental field through a distributed source, produced by the swarm. After proving an existence result for the solution of the optimal control problem, we discretize and solve the problem using the Finite Element Method (FEM). The FEM discretization naturally provides an operator that represents the bilinear way in which the controls enter into the dynamics of the vehicle swarm and the environmental field. Finally, we show through numerical simulations the effectiveness of our control strategy in regulating the environmental field to zero or to a desired distribution in the presence of a double-gyre flow field.
In this paper, we propose a computationally efficient, robust density control strategy for the me... more In this paper, we propose a computationally efficient, robust density control strategy for the mean-field model of a robotic swarm. We formulate a static optimal control problem (OCP) that computes a robot velocity field which drives the swarm to a target equilibrium density, and we prove the stability of the controlled system in the presence of transient perturbations and uncertainties in the initial conditions. The density dynamics are described by a linear elliptic advection-diffusion equation in which the control enters bilinearly into the advection term. The well-posedness of the state problem is ensured by an integral constraint. We prove the existence of optimal controls by embedding the state constraint into the weak formulation of the state dynamics. The resulting control field is space-dependent and does not require any communication between robots or costly density estimation algorithms. Based on the properties of the primal and dual systems, we first propose a method to accommodate the state constraint. Exploiting the properties of the state dynamics and associated controls, we then construct a modified dynamic OCP to speed up the convergence to the target equilibrium density of the associated static problem. We then show that the finite-element discretization of the static and dynamic OCPs inherits the structure and several useful properties of their infinite-dimensional formulations. Finally, we demonstrate the effectiveness of our control approach through numerical simulations of scenarios with obstacles and an external velocity field.
In this paper, we propose a fully decentralized control strategy for collective payload transport... more In this paper, we propose a fully decentralized control strategy for collective payload transport in 3D space by a team of identical holonomic mobile robots in a microgravity environment. This task has potential space applications such as on-orbit assembly, debris removal, and planetary construction, which have to be performed in uncertain environments where inter-robot communication is unreliable or not available. Decentralized control schemes that rely on limited data and do not require inter-robot communication would enable teams of robots to achieve cooperative transport objectives in unknown environments. Existing decentralized strategies for collective payload transport require at least some of the following information: (1) the geometry and dynamics of the payload; (2) the payload's position and velocity over time; (3) the number and distribution of robots around the payload; (4) the vector from the payload's center of mass to each robot's attachment point; and (5) desired trajectories for the robots and payload. In this paper, we consider a team of robots that must stabilize a payload's center of mass to a target position without access to any of this information. The robots are assumed to be rigidly attached to the payload, e.g. via pincers, grippers, or magnets, and the only information provided to them is the target position in a global coordinate system that is shared by all the robots. The robots do not exchange information and only require measurements of their own positions and velocities. Moreover, the payload may have an arbitrary shape, without particular constraints on its geometry (e.g., convexity). Given these assumptions and objectives, and building on our prior work on collective transport strategies, we design a fully decentralized proportional-derivative controller that can be employed by the robots to drive the payload's center of mass to the destination. Using a Lyapunov stability argument, we analytically prove that under this controller, the payload's center of mass asymptotically converges to a small neighborhood of the target position. The radius of this neighborhood is the magnitude of the error between the target position and actual steady-state position of the payload's center of mass. We also investigate the effect of the distribution of robots around the payload on the magnitude of this error. We validate our theoretical results in MATLAB simulations of five collective transport scenarios with different payload shapes and variations in the distribution of robots around the payload.
In this paper, we propose decentralized position controllers for a team of point-mass robots that... more In this paper, we propose decentralized position controllers for a team of point-mass robots that must cooperatively transport a payload to a target location. The robots have double-integrator dynamics and are rigidly attached to the payload. The controllers only require robots' measurements of their own positions and velocities, and the only information provided to the robots is the desired position of the payload's center of mass. We consider scenarios in which the robots do not know the position of the payload's center of mass and try to selfishly stabilize their own positions to the desired location, similar to the behaviors exhibited by certain species of ants when retrieving food items in groups. We propose a proportional-derivative (PD) controller that does not rely on inter-robot communication, prior information about the load dynamics and geometry, or knowledge of the number of robots and their distribution around the payload. Using a Lyapunov argument, we prove...
In this paper, we propose an obstacle avoidance controller for a disk-shaped holonomic robot with... more In this paper, we propose an obstacle avoidance controller for a disk-shaped holonomic robot with double-integrator dynamics and local sensing. The control objective is for the robot to converge to a target velocity while avoiding collisions with strictly convex obstacles in an unbounded environment. We assume that the robot has no information about the location and geometry of the obstacles, has no localization capabilities, and can only measure its own velocity and its relative position vector to the closest point on any obstacles in its sensing range. We first propose a potential-based controller for the case with a single obstacle, and we prove that the robot safely navigates past the obstacle and attains the desired velocity. For the case with multiple obstacles, we propose a switching control scheme in which the robot applies the single-obstacle controller for the closest obstacle at each instant. We investigate the correctness of this switching control law and demonstrate the absence of local stable equilibrium points that would trap the robot. We validate our analytical results through simulations of a robot that uses the proposed controllers to successfully navigate through an environment with strictly convex obstacles of various shapes and sizes.
This paper presents a novel procedure for computing parameters of a robotic swarm that guarantee ... more This paper presents a novel procedure for computing parameters of a robotic swarm that guarantee coverage performance by the swarm within a specified error from a target spatial distribution. The main contribution of this paper is the analysis of the dependence of this error on two key parameters: the number of robots in the swarm and the robot sensing radius. The robots cannot localize or communicate with one another, and they exhibit stochasticity in their motion and task-switching policies. We model the population dynamics of the swarm as an advection-diffusion-reaction partial differential equation (PDE) with time-dependent advection and reaction terms. We derive rigorous bounds on the discrepancies between the target distribution and the coverage achieved by individualbased and PDE models of the swarm. We use these bounds to select the swarm size that will achieve coverage performance within a given error and the corresponding robot sensing radius that will minimize this error. We also apply the optimal control approach from our prior work in [13] to compute the robots' velocity field and task-switching rates. We validate our procedure through simulations of a scenario in which a robotic swarm must achieve a specified density of pollination activity over a crop field.
In this work, we analyze stochastic coverage schemes (SCS) for robotic swarms in which the robots... more In this work, we analyze stochastic coverage schemes (SCS) for robotic swarms in which the robots randomly attach to a onedimensional boundary of interest using local communication and sensing, without relying on global position information or a map of the environment. Robotic swarms may be required to perform boundary coverage in a variety of applications, including environmental monitoring, collective transport, disaster response, and nanomedicine. We present a novel analytical approach to computing and designing the statistical properties of the communication and sensing networks that are formed by random robot configurations on a boundary. We are particularly interested in the event that a robot configuration forms a connected communication network or maintains continuous sensor coverage of the boundary. Using tools from order statistics, random geometric graphs, and computational geometry, we derive formulas for properties of the random graphs generated by robots that are independently and identically distributed along a boundary. We also develop order-of-magnitude estimates of these properties based on Poisson approximations and threshold functions. For cases where the SCS generates a uniform distribution of robots along the boundary, we apply our analytical results to develop a procedure for computing the robot population size, diameter, sensing range, or communication range that yields a random communication network or sensor network with desired properties.
Experimental Study and Modeling of Group Retrieval in Ants as an Approach to Collective Transport in Swarm Robotic Systems This study finds that ants can act independently to accomplish complex tasks; application of models derived from ant behavior to robotic systems is investigated
2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2011
We present a scalable approach to optimizing robot control policies for a target collective behav... more We present a scalable approach to optimizing robot control policies for a target collective behavior in a spatially inhomogeneous robotic swarm. The approach can incorporate robot feedback to maintain system performance in an unknown environmental flow field. We consider systems in which the robots follow both deterministic and random motion and transition stochastically between tasks. Our methodology is based on an abstraction of the swarm to a macroscopic continuous model, whose dimensionality is independent of the population size, that describes the expected time evolution of swarm subpopulations over a discretization of the environment. We incorporate this model into a stochastic optimization method and map the optimized model parameters onto the robot motion and task transition control policies to achieve a desired global objective. We illustrate our methodology with a scenario in which the behaviors of a swarm of robotic bees are optimized for both uniform and nonuniform pollination of a blueberry field, including in the presence of an unknown wind.
We do a Probabilistic Analysis of the Network generated by robots involved in Stochastic Boundary... more We do a Probabilistic Analysis of the Network generated by robots involved in Stochastic Boundary Coverage
Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective t... more Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective transport strategies that are decentralized, scalable, and do not require a priori information about the payload. We investigate this phenomenon in Aphaenogaster cockerelli in order to extract the ants' roles during transport, the rules that govern their actions, and the individual forces that they apply to guide a food item to their nest. To measure these forces, we designed and fabricated elastic structures with calibrated stiffness properties, induced ants to retrieve the structures, and tracked the resulting deformations with a camera. We then developed a hybrid system model of the ant behaviors that were observed in the experiments. We conducted simulations of the behavioral model that incorporate a quasistatic model of planar manipulation with compliant attachment points. Our simulations qualitatively replicate individual ant activity as well as certain macroscopic features of the transport.
We present a new algorithm for the reachability analysis of multi-affine hybrid systems. In our p... more We present a new algorithm for the reachability analysis of multi-affine hybrid systems. In our previous work on reachability analysis and that of our collaborators [1-3], we exploited the convexity of multiaffine functions and the fact that the vector field in modes with rectangular invariants is uniquely determined by its values at the rectangle vertices. In this paper, we explicitly calculate conical overapproximations of the reachable set in the invariant of each mode. We describe our Multi-Affine Reachability analysis using Conical Overapproximations, Marco, and show that it yields results that are superior to those obtained by existing methods for multi-affine hybrid systems. Finally, we demonstrate the application of Marco to the analysis of an ant house hunting model that incorporates quorum sensing [4] and the analysis of bi-stability of the lactose induction system regulated by glucose and lactose [5].
Proceedings of the 16th international conference on Hybrid systems: computation and control, 2013
Collective food transport in ant colonies is a striking, albeit poorly understood, example of coo... more Collective food transport in ant colonies is a striking, albeit poorly understood, example of coordinated group behavior in nature that can serve as a template for robust, decentralized multi-robot cooperative manipulation strategies. We
We present a methodology for characterizing, analyzing, and synthesizing swarm behaviors using bo... more We present a methodology for characterizing, analyzing, and synthesizing swarm behaviors using both a macroscopic continuous model that represents a swarm as a continuum and a macroscopic discrete model that enumerates individual agents. Our methodology is applied to a dynamical model of ant house hunting, a decentralized process in which a colony attempts to emigrate to the best site among several alternatives. The model is hybrid because the colony switches between different sets of behaviors, or modes, during this process. Using the model in [1], we investigate the relation of site population growth to initial system state with an algorithm called Multi-Affine Reachability analysis using Conical Overapproximations (Marco) [2]. We then derive a microscopic hybrid dynamical model of an agent that respects the specifications of the global behavior at the continuous level. Our multi-level simulations demonstrate that we have produced a rigorously correct microscopic model from the macroscopic descriptions.
Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
We present a methodology for characterizing and synthesizing swarm behaviors using both a macrosc... more We present a methodology for characterizing and synthesizing swarm behaviors using both a macroscopic model that represents a swarm as a continuum and a microscopic model that represents individual robots. We develop a systematic approach for synthesizing behaviors at the macroscopic level that can be realized on individual robots at the microscopic level. Our methodology is inspired by a dynamical model of ant house hunting [1], a decentralized process in which a colony attempts to emigrate to the best site among several alternatives. The model is hybrid because the colony switches between different sets of behaviors, or modes, during this process. At the macroscopic level, we are able to synthesize controllers that result in the deployment of a robotic swarm in a predefined ratio between distinct sites. We then derive hybrid controllers for individual robots using only local interactions and no communication that respect the specifications of the global continuous behavior. Our simulations demonstrate that our synthesis procedure yields a correct microscopic model from the macroscopic description with guarantees on performance at both levels.
2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2007
We present an approach for the dynamic assignment and reassignment of a large team of homogeneous... more We present an approach for the dynamic assignment and reassignment of a large team of homogeneous robotic agents to multiple locations with applications to search and rescue, reconnaissance and exploration missions. Our work is inspired by experimental studies of ant house hunting and empirical models that predict the behavior of the colony that is faced with a choice between multiple candidate nests. We design stochastic control policies that enable the team of agents to distribute themselves between multiple candidate sites in a specified ratio. Additionally, we present an extension to our model to enable fast convergence via switching behaviors based on quorum sensing. The stability and convergence properties of these control policies are analyzed and simulation results are presented.
2008 47th IEEE Conference on Decision and Control, 2008
We present a decentralized, communication-less approach to the dynamic allocation of a swarm of h... more We present a decentralized, communication-less approach to the dynamic allocation of a swarm of homogeneous robots to a target distribution among multiple sites. Building on our work in [1], we optimize stochastic control policies for the robots that cause the population to quickly redistribute among the sites while adhering to a limit on inter-site traffic at equilibrium. We propose a way to account for delays due to navigation between sites in our controller synthesis procedure. Control policies that are designed with and without the use of delay statistics are compared for a simulation in which 240 robots distribute themselves among four buildings.
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Papers by Spring Berman